Generation of short-wave ultrashort light pulses and use thereof

ABSTRACT

Extremely ultrashort and short-wave light pulses are generated with the aid of the traveling-wave Thomson scattering process. Dispersive elements are arranged between an electron, particle, or radiation source, which is synchronized with a laser system, and an optical element that focuses in a direction. The device is used to superpose a pulse-front tilted light pulse of high power with an ultrashort pulse of relativistic electrons in a laser-line focus. By varying the laser pulse-front tilt, narrow-band radiation pulses in a wide wavelength range from EUV to X-ray wavelengths and having a high number of protons are obtained, and the bandwidth and coherence properties can also be modified. The system can be used, among other things, in EUV lithography, in the planning and optimal design of laser systems and electron sources, in material analysis by phase contrast imaging, and in superconductor research. The assembly is smaller and cheaper than current comparables.

The application describes a system for generating (very) short-wave ultra-short light pulses and the resulting possible uses.

Thomson scattering of laser sources is limited so far by two parameters, once the interaction length between the laser and electrons and the other, the maximum laser intensity.

The length of the interaction is determined by the Rayleigh length, usually in the range of several micrometers, which may be extended only by lower radial focusing of the laser.

En even smaller fraction of the laser light interacts with the electrons by extension of Rayleigh length for a given electron beam diameter, thereby, the efficiency is drastically reduced. Furthermore, by increasing the laser intensity, the number of photons in a narrow energy band cannot any be increased, because this leads to the disturbance of the electron trajectories on basis of non-linear laser-electron interaction and thus to produce higher frequencies. Therefore, based on Thomson scattering sources, were planned especially for highly repetitive laser systems with low peak power and high average power.

This provides nevertheless no temporally coherent pulses and few photons per single shot.

In the range of EUV and XUV, pluralities of competing source concepts exist because of the important lithographic application by reduction of semiconductor structures. In particular, the laser-driven nonlinear generation of shorter wavelengths in gases and the high harmonic generation using laser-plasma interaction are mentioned. These sources provide ultra-short light pulses with laser-like properties, but do not have high single-shot performance. Moreover, these systems are difficult scalable to higher photon energies and they have problems with avoidance of debris by high average power due to the use plasmas, because debris limits the lifetime of the used optics. Other types of sources for the wavelength range from EUV to XUV are characterized by high divergence and not enough photons reach the target wavelength. [Jonkers, J.: High power extreme ultra-violet (EUV) light sources for future lithography. Plasma Sources Science and Technology (15) 2006. pp. 8-16.]

In the field of X-ray, competing systems are existing storage ring-based X-ray sources of the fourth generation, like the ESRF (European Synchrotron Radiation Facility) or the ring accelerator PETRA at DESY. These, however, provide neither comparable nor short pulses and they do not allow it a wide tunability of the wavelength.

The number of photons per shot is also not very high and the radiation lacks the temporal coherence. The size of these facilities and the level of associated operating costs make this infrastructure very expensive, stuff intensive and inflexible in adapting to new requirements.

Thomson sources like PLEIADES [Hartemann, F. V. et al.: Compton scattering and its applications: The PLEIADES Femtosecond X-ray source at LLNL. International Workshop on Quantum Aspects of Beam Physics, Hiroshima, Japan, Jan. 7, 2003-Jan. 10, 2003] or like NewSUBARU [Amano, S. et al: Several-MeV γ-ray generation at NewSUBARU by laser-Compton backscattering. Nuclear Instruments and Methods in Physics Research A 602 (2009). pp. 337-341] generate hard, monochromatic X-rays, and have much lower requirements with respect to the required electron energies, because laser pulses are used as optical undulators. However, the number of photons per shot is also not very high and the radiation lacks the temporal coherence. These systems also scale poorly to higher peak power lasers.

High photon numbers per pulse deliver far only free electron laser (FEL) as FLASH or LCLS. Even more than storage rings are FELs large systems with all the attendant disadvantages, in terms of size and cost of the infrastructure [Pellegrini, C. et al: The Development of X-Ray Free-Electron Lasers. IEEE Journal of Selected Topics in Quantum Electronics (19), 2004, No. 6, pp. 1393-1404.]. Compact (table-top) SASE FEL use laser-driven electron sources (ultra-short pulses of electrons with large charge per pulse through so-called laser Wakefield acceleration); these systems are not very flexible in terms of tunability of the photon energies. The generation of strong alternating fields within the Undulator structure due to so-called Wakefield's (resistive feedback from Undulator walls) is an equally unresolved problem in the previously existing concept studies, such as the appropriate micro-focusing of the electron beams. [Grüner, F. et al.: Design considerations for table-top, laser-based VUV and X-ray free electron lasers. Appl. Phys. B: Lasers and Optics (86), 2007, pp. 431-435].

Bragg structures allow an efficient coupling of the laser field with a pulsed electron beam, which are placed on the electron properties technically difficult to fulfill requirements. [Karagodsky, V. et al.: Enhancing X-Ray Generation by Electron-Beam Laser Interaction in at Optical Bragg Structure. Physical Review Letters (104) 2010, pp. 024801].

[Telnov, V.: Laser Cooling of Electron Beams for Linear Collider. Physical Physics Letters (78) 1997 No. 25, pp. 4757-4760] describes the radiated cooling of electron beams.

Object of the invention is the generation of short-wave and ultra-short light pulses of a radiation source, wherein the light pulses have better properties. The laser should be optimally highly compressed in time on the entire interaction region, to increase interaction efficiency. Under ultra-short laser pulses can be understood laser pulses less than 1 ps and with ultra-short electron pulses are mean pulses less than 10 ps. In the application, interaction region means the area wherein the overlap between electron pulse and laser pulse is given during the complete time.

The object is achieved by an arrangement according to the first claim, which has been adapted to use with the Traveling Wave Thomson scattering method for ultra-short pulses. The Traveling Wave Thomson Scattering method (TWTS) is used with special dispersive elements. These dispersive elements should realize the optimum temporal and spatial pulse compression of the laser pulse in the overlap region at each time point of interaction with the electron pulse into an interaction region of a length of a millimeter to several meters.

The inventive arrangement can be built and can be operated with less effort and low cost. When using the inventive arrangement with a given bandwidth, a greater yield of photons as using other arrangements is obtained.

Advantageous embodiments and applications are given in the additional claims, which are described and shown using figures:

FIG. 1 shows inventive arrangement and functioning

-   -   a) Generating a laser line focus so, that the spatial overlap of         the electron pulse with the laser line focus is ensured over a         period of the interaction region,     -   b) Wave fronts in lateral Thomson scattering geometry,     -   c) Tilted laser pulse front in the overlap with an electron         pulse

FIG. 2: 3D display, illustrating the optimal spatial and temporal pulse compression

FIG. 3: Illustration of two light pulses at different time points using for the optimal spatial and temporal pulse compression with a dispersive element

FIG. 4: optical layout of a TWTS source

FIG. 5 uniform grating (top) and with variable grating spacings (below)

FIG. 6: geometrical relationship between reflection of the laser pulse at a (VLS) and the grating dispersion control at optimal spatial and temporal chirp

FIG. 7: Ring accelerator coupled with a TWT-FEL in a resonator

Existing Thomson and Compton resources have a scaling problem in a high photon yield per pulse. There exists a maximum laser intensity that may not be exceeded; otherwise the non-linear effects prevent the efficient backscattering in a single narrow photon energy interval.

This allows high photon fluxes can only be achieved over a long distance of interaction between lasers with longer pulse duration and the electrons. However, by the strength of the focusing of the laser, there is a relationship between the focus size and Rayleigh length, which determines the maximum interaction distance. Rayleigh length is longer, than the focus diameter is greater. Thus, it is not possible both for conventional Thomson sources, i.e. to realize small interaction diameter for optimal overlap with electron pulses and to realize long interaction diameter at the same time. Greater focus diameter lead to lower intensities and, subsequently of the scattered radiation, to lower photon fluxes.

In accordance with the invention adapted TWTS method, optical reflection, gratings are used in conjunction with cylindrical mirrors for generating a pulse front tlit of the laser pulse and for generating a long line of focus. Compared to conventional Thomson scattering, the inventive TWTS method with its special dispersive elements solves the problem of limiting the interaction length and as well the problem of the limitation of the laser pulse intensity.

The special feature of the designed by the inventive method TWTS sources is that an efficient coupling of the laser field is achieved by a pulsed electron beam, and that the variation of the wavelength of the radiation and its bandwidth over a wide range without changing the laser system or the electron source is possible. With this decrease both cost and effort for the adaptation to the requirements of potential users enormously over currently available sources for the generating of short-wave light pulses.

To bypass the Rayleigh limit, an optical structure is required, in which the electrons do not leave the focal region of the laser. This is possible, for example, cylindrical lenses, wherein the laser is focused only in one direction to a line. Now, if the electrons propagate along this line, such as in FIG. 1 a, they remain over the entire width of the laser beam in the focal region. This implies, however, a side scattering geometry with a side scattering angle or an interaction angle φ between 0° and 180° [deg.], see FIG. 1 b. However, this leads to that laser and electrons propagate in different non-collinear directions, so that in these scenarios, the spatial overlap is normally lost for short distances which are comparable to the laser and/or electron beam dimensions. A solution of the problem is the tilt of the laser pulse front by a predetermined angle α, with the aim that always an overlap region of the laser and the electron exists in spite of the beam propagation (see FIG. 1 c). The tilt angle results, that the envelope of the laser pulse follows the electrons, so that they will stay stationary in relation to the temporal envelope of the laser. This area of overlap is called central interaction region.

The tilting of the laser pulse, changes only the envelope, but not the wave fronts, which determines the frequency of the scattered light. The pulse front tilt leads to a position dependent propagation delay which shifts the envelope of the laser relative to the phase of the carrier wave (carrier phase). For relativistic electron energies are α≅φ/2.

In laboratory reference system the electrons are exposed the carrier frequency of the laser divided by the geometric factor (1−cos φ). In FIG. 2 is summarized the whole principle of such Thomson source in a graph, wherein laser and electron beam positions are shown at three different times, at the beginning 1, in the middle 2 and at the end of the scattering interaction 3. The combination of three different geometries are shown: the focal line along the electron beam, the side scattering with the interaction angle φ and tilted pulse front by the angle α≅φ/2. Further the figure shows, how the entire laser beam slides successively through the electron pulse in the course of interaction, so that all components of the laser pulse interact with the electrons. The electrons, and thus the X-ray pulse are continuously pumped by the laser, while both propagate equally along the line focus.

During the propagation of the laser pulse with a tilted pulse front over a distance, the spatial dispersion (spatial dispersion SD) and the group delay dispersion (group delay dispersion GDD) are changed due to the angular dispersion (axial suspension AD). The spatial dispersion SD (x) varies linearly along the transverse laser pulse coordinate SD(x)=AL(x)−AD (see FIG. 3). Because these dispersion effects have a major influence on the pulse structure of ultrashort laser pulses, it is usually necessary to compensate for this dispersion in the optical design using additional dispersive elements.

The optical part of TWTS (FIG. 4) begins with a laser system which makes available stretched laser pulses with defined spatial dispersion over a stretching-compressor system. The final grate 10 causes the required pulse front tilt of φ/2. The angular dispersion which is caused by the grating, compresses the laser pulse in following always until maximum pulse compression and spatial dispersion is achieved in the vanishing line focus of the optical assembly. This grating (varied line-spacing (VLS) grating) has varying grating spacing so that the dispersion does not disappear only at a single time, but spatially along the entire line focus. The dispersive element is designed as a VLS grating, the VLS grating causes spatial and temporal dispersion compensation. This achieves an optimal temporal compression of the laser pulse in the overlapping area at any time of the interaction and thus the entire interaction region. This provides an increase in the scattering efficiency.

Investigations have shown that the order of the optical elements focusing element and dispersive element is no matter if the dispersions are compensated in the overlapping region according to the equations (Eq. 3), (Eq. 4) and (Eq. 6). The optimal spatial and temporal pulse compression is therefore ensured.

Grating compressors compensate spatial dispersion by lattice pairs or grating pairs. Because the laser pulse propagates non-negligible distances ΔL>π(cτ₀)²/(λ₀ tan² α) at large angles φ during interaction with the electrons, this compensation method is not enough. To avoid loss of efficiency due to the longer laser pulse durations and frequency chirp in the scattered radiation, the spatial dispersion of the laser should be zero over the entire interaction distance, and not only at a specific time. Therefore, optical gratings first order, i.e. gratings without position dependence, cannot be used.

For an electron pulse, which is overlaid with a tilted laser pulse, is

SD(x)=ΔL(x)·AD,  (Eq. 1)

wherein SD (x) means the spatial dispersion and AD means the constant angular dispersion.

The x-coordinate is the transverse position deviation from the central ray. Due to the pre-compensation of the dispersion with an additional spatial grating pair is SD (0)=0, and ΔL(0)=0. The laser propagates at a further distance ΔL(x), if the electrons move in the x direction along the laser pulse front, so that the spatial dispersion SD (x) is no longer zero. To compensate the spatial dispersion SD (x) it should apply:

SD′(x)=∂² x _(out) /∂Δv∂x _(in)≠0.  (Eq. 2)

Therefore, no first-order approximations can be assumed because the required optics contains non-negligible higher order derivatives in x.

The following dispersion conditions are all derived with the basic TWTS design principles:

-   -   1. The change in spatial dispersion SD(x,t)=∂x_(out)/∂Δv along         the electron trajectory x_(el)(t) and hence across the laser         beam diameter should compensate the spatial dispersion, which         was acquired through the laser propagation distance ΔL(x) to the         interaction line. Thus obtained an efficient overlap with the         electrons and an optimum laser compression (see FIG. 3). Because         laser propagation distance ΔL(x) is defined by the difference in         slopes of electron bunch trajectory and laser pulse front tilt         with respect to the wave front, it is defined:

$\begin{matrix} \left. {{SD}\left( {x,t} \right)} \middle| {}_{x = {x_{el}{(t)}}}{\equiv {{{SD}\left( {{x_{el}(t)},0} \right)} - {{{{AD}\left( {x_{el}(t)} \right)} \cdot \Delta}\; {L\left( {x_{el}(t)} \right)}}}\frac{\pi \; c\; \tau_{0}^{2}}{\tan \; {\varphi/2}}} \right. & \left( {{Eq}.\mspace{14mu} 3} \right) \\ {\mspace{79mu} {{\Delta \; {L(x)}} = {\left( {{\tan \left( {{\pi/2} - \varphi} \right)} + {\tan \left( {\varphi/2} \right)}} \right) \cdot x}}} & \left( {{Eq}.\mspace{14mu} 4} \right) \end{matrix}$

The required pulse front tilt PFT(x)=c·(∂Δt(x)/∂x) needs to be constant across the entire laser pulse, so that the pulse front is not hidden,

c·Δt(x)−x·tan φ/2<<cτ ₀.  (Eq. 5)

-   -   2. The temporal profile of the laser should not change, so the         group delay GDD is less than the transform limited pulse         duration:

$\begin{matrix} {{{{GDD}\left( {x,t} \right)}_{x = {x_{el}{(t)}}}{\Delta \; v_{0}}} = {\frac{{\partial\Delta}\; {t_{out}\left( {x,t} \right)}}{{\partial\Delta}\; v}_{x = {x_{el}{(t)}}}{\Delta \; v_{0}{\; {{c\; \tau_{0}},}}}}} & \left( {{Eq}.\mspace{14mu} 6} \right) \end{matrix}$

-   -   -   which can be expressed for general temporal pulse shapes, as             well as for non-linearly chirped pulses as

$\begin{matrix} {{\langle\left( {{\frac{\Delta \; v}{2\pi}{{GDD}\left( {x,t,{\Delta \; v}} \right)}}_{x = {x_{el}{(t)}}}} \right)^{2}\rangle}_{\Delta \; v}{{{\langle\tau_{0}^{2}\rangle}.}}} & \left( {{Eq}.\mspace{14mu} 7} \right) \end{matrix}$

The in FIG. 4 shown structure realizes a pre-compensation of the spatial dispersion (SD) and of the group delay dispersion (GDD) for the dispersion of the beam from the grating to the interaction region by an additional grating combination at the beginning of the arrangement. This type of SD and GDD compensation is standard technology and is widely used in optical stretchers and compressors for CPA lasers (chirped pulse amplification laser).

The two dispersions SD and GDD are fulfill the conditions of the equations (Eq. 3), (Eq. 4) and (Eq. 6), and they have to disappear not only at a certain time of the laser beam propagation, but must be sufficiently small or disappear on the respective current electron pulse position along the interaction distance, if they will. In the arrangement of FIG. 4, a VLS grating with a square grating spacing chirp as the last grid is used for compensation. Thus, an additional angular dispersion

AD(x)=AD ₀ +SD ₀ ·C ₁ ·x,  (Eq. 8),

is realized, which varies linearly over the laser beam diameter, so that the condition for the linear spatial dispersion (Eq. 3) in the line focus of the last propagation distance L₀= ABC is realized. AD₀ and the product SD₀·C₁ are constant parameters that are defined by design.

In an existing laser system and an electron source, a suitable combination of the grating with the corresponding grating distances and angles can be determined between the gratings. The determination of the grating spacing is made on the basis of ray tracing with the help of Kostenbauder formalism of higher order.

The cylindrical mirror (see FIG. 4) focuses only in one dimension, thereby; it is possible to reduce the description of plane waves in two dimensions. Thus, the parallel to the level of interaction extending wavefront be neglected, wherein, the level of interaction is spanned by the directions of the laser and electron beam. The laser pulse in 2D can be described using a raytracing approach, because all gratings introduce dispersions parallel to the same manner, at each level to the level of interaction.

An optical system fist order can be described by a 4×4—matrix M with beam input and output components (position x, angle θ, time delay Δt, frequency derivation Δv in relation to a center beam, according to Kostenbauder [Kostenbauder, A. G.: Raypulse matrices: a rational treatment for dispersive optical system. IEEE Journal of Quantum Electronics 26 (1990). pp. 1148-1157]

$\begin{matrix} {\begin{pmatrix} x_{out} \\ \theta_{out} \\ {\Delta \; t_{out}} \\ {\Delta \; v} \end{pmatrix} = {\underset{\underset{M}{}}{\begin{pmatrix} \frac{\partial x_{out}}{\partial x_{in}} & \frac{\partial x_{out}}{\partial\theta_{in}} & 0 & \frac{\partial x_{out}}{{\partial\Delta}\; v} \\ \frac{\partial\theta_{out}}{\partial x_{in}} & \frac{\partial\theta_{out}}{\partial\theta_{in}} & 0 & \frac{\partial\theta_{out}}{{\partial\Delta}\; v} \\ \frac{{\partial\Delta}\; t_{out}}{\partial x_{in}} & \frac{{\partial\Delta}\; t_{out}}{\partial\theta_{in}} & 1 & \frac{{\partial\Delta}\; t_{out}}{{\partial\Delta}\; v} \\ 0 & 0 & 0 & 1 \end{pmatrix}} \cdot \begin{pmatrix} x_{in} \\ \theta_{in} \\ {\Delta \; t_{in}} \\ {\Delta \; v} \end{pmatrix}}} & \left( {{Eq}.\mspace{14mu} 9} \right) \\ \begin{matrix} {M = \begin{pmatrix} A & B & 0 & E \\ C & D & 0 & F \\ G & H & 1 & I \\ 0 & 0 & 0 & 1 \end{pmatrix}} \\ {= \begin{pmatrix} {{spatitial}\mspace{14mu} {{magn}.}} & {{offset}\mspace{14mu} {by}\mspace{14mu} {angle}} & 0 & {SD} \\ {focus} & {{angular}\mspace{14mu} {{magn}.}} & 0 & {AD} \\ {{puls}\mspace{14mu} {front}\mspace{14mu} {tilt}} & {{time}\text{-}{angle}} & 1 & {GDD} \\ 0 & 0 & 0 & 1 \end{pmatrix}} \end{matrix} & \left( {{Eq}.\mspace{14mu} 10} \right) \end{matrix}$

Using plane waves the matrix elements of M represents direct physical meanings, such as spatial magnification for element A or group delay dispersion (GDD) for the element I. For variable gratings (line spacing varied—VLS), this approach leads to not negligible higher order terms in the ray coordinate x_(in).

For a general, planar grating, it is necessary to derive the behavior of the spatially displaced rays and include the position dependencies in all other relations including the grating constant. In FIG. 6, the ray displaced by a distance x_(in) hits the VLD grating at the grating surface coordinates s= AB−x_(in)/cos ψ_(in), which determines an diffraction angle ψ_(out)(x_(in)) different from the central ray output angle ψ_(out,0). The two reference planes (shown in FIG. 6) represent the wave fronts of the ingoing and the outgoing beam. All changes to the beam characteristics are considered in relation to the central ray and its reference plane. The resulting spatial displacement with respect to the central means AC and the temporal delay is the difference ( DB− BC)/c. Using FIG. 6 now can write for following angular relationships: α=ψ_(out,0), β=π/2−ψ_(out)(x _(in)) and γ=π/2−(ψ_(out,0)−ψ_(out)(x _(in))). With the sine theorem we find

$\begin{matrix} \begin{matrix} {{A{\left( x_{in} \right) \cdot x_{in}}} = \overset{\_}{AC}} \\ {= {{- \frac{\cos \; {\psi_{out}\left( x_{in} \right)}}{\cos \; \left( {\psi_{{out},0} - {\psi_{out}\left( x_{in} \right)}} \right)}} \cdot \frac{x_{in}}{\cos \; \psi_{in}}}} \end{matrix} & \left( {{Eq}.\mspace{14mu} 11} \right) \\ \begin{matrix} {{{G\left( x_{in} \right)} \cdot x_{in}} = {\left( {\overset{\_}{DB} - \overset{\_}{BC}} \right)/c}} \\ {= {\frac{\sin \; \psi_{{out},0}}{\cos \; \left( {\psi_{{out},0} - {\psi_{out}\left( x_{in} \right)}} \right)} \cdot \frac{x_{in}}{{c \cdot \cos}\; \psi_{in}}}} \end{matrix} & \left( {{Eq}.\mspace{14mu} 12} \right) \end{matrix}$

VLS gratings have focusing properties because the angle of ψ_(out) changes with position at which the beam incidents on the grating surface. Thus, the following applies:)

C(x _(in))·x _(in)=ψ_(out,0−ψ) _(out)(x _(in)).  (Eq. 13)

The angular magnification D(x_(in))=∂θ_(out)/∂θ_(in) and the angular dispersion F(x_(in))=∂Δt_(out)/∂Δv_(in) are both derivatives of the grating equation:

D(x _(in))=−(∂ψ_(out)(x _(in))/∂ψ_(in))  (Eq. 14)

F(x _(in))=−(∂ψ_(out)(x _(in))/∂v)  (Eq. 15)

The matrix elements are B(x_(in))=E(x_(in))=H(x_(in))=I(x_(in))=0, because the rays reflect at the grating surface with no time delay or spatial displacement.

Using the equations of the grating distance function d(s)=d₀+a_(g)λ₀s+b_(g)λ₀s², the grating equation ψ_(out)(x_(in))=arcsin(c/(v·d(x _(in)/cos ψ_(in)))+sin ψ_(in)) and the above relations, the matrix elements can be write as:

$\begin{matrix} {{A\left( x_{in} \right)} = {{{- \cos}\; {\psi_{out}/\cos}\; \psi_{in}} + {a_{g}x_{in}\tan \; {\psi_{out} \cdot \left( {{\tan \; \psi_{in}} - {\sin \; {\psi_{out}/\cos}\; \psi_{in}}} \right)^{2}}}}} & \left( {{Eq}.\mspace{14mu} 16} \right) \\ {{C\left( x_{in} \right)} = {{{- a_{g}}\frac{\left( {{\sin\left( \; \psi_{in} \right)} - {\sin\left( \; \psi_{out} \right)}} \right)^{2}}{\cos \; \left( \psi_{in} \right)\cos \; \left( \psi_{out} \right)}} + {{x_{in}\left( {{4b_{g}} + {4b_{g}\cos \; \left( {2\psi_{out}} \right)} + {8a_{g}^{2}{\sin \left( \psi_{in} \right)}} - {a_{g}^{2}x\; {\sin \left( {{2\psi_{in}} - \psi_{out}} \right)}} - {7a_{g}^{2}\sin \; \psi_{out}} - {a_{g}^{2}\; {\sin \left( {3\psi_{out}} \right)}} + {a_{g}^{2}\; {\sin \left( {{2\psi_{in}} + \psi_{out}} \right)}}} \right)} \cdot {\left( {{\tan \; \psi_{in}} - {\sin \; {\psi_{out}/\cos}\; \psi_{in}}} \right)^{2}/\left( {8\cos^{3}\psi_{out}} \right)}}}} & \left( {{Eq}.\mspace{14mu} 17} \right) \\ {{D\left( x_{in} \right)} = {{{- \cos}\; {\psi_{in}/\cos}\; \psi_{out}} - {a_{g}{{x_{in}\left( {{\cos^{2}\psi_{out}\sin \; \psi_{in}} + {\cos^{2}\psi_{in}\sin \; \psi_{out}}} \right)} \cdot {\left( {{\tan \; \psi_{in}} - {\sin \; {\psi_{out}/\cos}\; \psi_{in}}} \right)^{2}/\cos^{3}}}\psi_{out}}}} & \left( {{Eq}.\mspace{14mu} 18} \right) \\ {{F\left( x_{in} \right)} = {\left( {\lambda_{0}/{c\left( {{\tan \; \psi_{out}} - {\sin \; {\psi_{in}/\cos}\; \psi_{out}}} \right)}} \right) - {a_{g}x_{in}{{\lambda_{0}/{c\left( {{\sin \; \psi_{in}} - {\sin \; \psi_{out}}} \right)}^{2}} \cdot {\left( {{\sin \; \psi_{in}} - {\sin \; \psi_{out}} - 1} \right)/\left( {\cos \; \psi_{in}\cos^{3}\; \psi_{out}} \right)}}}}} & \left( {{Eq}.\mspace{14mu} 19} \right) \\ {\mspace{79mu} {{G\left( x_{in} \right)} = {\left( {{{- \sin}\; {\psi_{out}/\cos}\; \psi_{in}} + {\tan \; \psi_{in}}} \right)/{c.}}}} & \left( {{Eq}.\mspace{14mu} 20} \right) \end{matrix}$

The grating chirps are mostly small and non-oscillatory nature. Thus the system can be described as a non-linear vector function

v _(out) =O _(VLS)(v _(in)).

which operates on the input ray vector v_(in)=(x_(in),θ_(in),Δt_(in),Δv). Because the nonlinearity of O_(VLS) exists only in the spatial displacement coordinate x_(in), it remains linear in the other coordinates. Therefore, the structures of the new operator still locally a Kostenbauder matrix:

x _(out)(x _(in),θ_(in) ,Δv)=A(x _(in))·x _(in) +B(x _(in))·θ_(in) +E(x _(in))·Δv  (Eq. 22)

θ_(out)(x _(in),θ_(in) ,Δv)=C(x _(in))·x _(in) +D(x _(in))·θ_(in) +F(x _(in))·Δv  (Eq. 23)

Δt _(out)(x _(in),θ_(in) ,Δt _(in) ,Δv)=G(x _(in))·x _(in) +H(x _(in))·θ_(in) +Δt _(in) +I(x _(in))·Δv  (Eq. 24)

Δv=Δv _(in) =Δv _(out) and B(x _(in))=E(x _(in))=H(x _(in))=I(x _(in))=0  (Eq. 25)

In the limit of uniform gratings, where is a_(g) and b_(g)→0, the Kostenbauder matrix simplifies for a standard grid to:

$\begin{matrix} {M_{g} = {\begin{pmatrix} {- \frac{\cos \; \psi_{out}}{\cos \; \psi_{in}}} & 0 & 0 & 0 \\ 0 & {- \frac{\cos \; \psi_{in}}{\cos \; \psi_{out}}} & 0 & \frac{\lambda_{0}\left( {{\sin \; \psi_{out}} - {\sin \; \psi_{in}}} \right)}{c\; \cos \; \psi_{out}} \\ \frac{{\sin \; \psi_{in}} - {\sin \; \psi_{out}}}{c\; \cos \; \psi_{out}} & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}.}} & \left( {{Eq}.\mspace{14mu} 26} \right) \end{matrix}$

The operators are sequentially applied to the input rays for individual embodiments:

v _(out) =M _(p)(s)·O _(VLS)(ψ_(in),ψ_(out) ,b _(g))(M _(gen)(SD,GDD)·v _(in)),  (Eq. 27)

wherein the second factor of (EEg.27) denotes the non-linear part of the system that operates on non-delayed, collimated input rays. The matrix M_(gen) represents the first order of a general stretcher/compressor system (see FIG. 4) with a defined group delay dispersion (GDD) and spatial dispersion (SD):

$\begin{matrix} {{M_{gen}\left( {{SD},{GDD}} \right)} = \begin{pmatrix} 1 & 0 & 0 & {SD} \\ 0 & 1 & 0 & 0 \\ 0 & {- {SD}} & 1 & {GDD} \\ 0 & 0 & 0 & 1 \end{pmatrix}} & \left( {{Eq}.\mspace{14mu} 28} \right) \end{matrix}$

The Kostenbauder matrix for free propagation M_(P)(L) is determined by

$\begin{matrix} {{M_{p}(L)} = {\begin{pmatrix} 1 & L & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}.}} & \left( {{Eq}.\mspace{14mu} 29} \right) \end{matrix}$

The combined operator expression of (Eq. 27) does not depend solely on the spatial displacement coordinate x_(in), but on all input ray coordinates. In the case of a collimated input beam (Δx_(in),0,0,Δv), the output beam components (x_(out)(x_(in),Δv),θ_(out)(x_(in),Δv),Δt_(out)(x_(in),Δv),Δv) denote to higher order polynomials in x_(in) and Δv, wherein the coefficients are functions of the parameters of the optical setup or design.

For the design of optical systems using the VLS grating, it is useful to reduce the complexity of the grating function. According, the focusing element in in (Eq. 10) simplifies to

$\begin{matrix} {{C\left( x_{in} \right)} = {{{- a_{g}}\frac{\left( {{\sin \left( \psi_{in} \right)} - {\sin \left( \psi_{out} \right)}} \right)^{2}}{{\cos \left( \psi_{in} \right)}{\cos \left( \psi_{out} \right)}}} + {{O\left( x_{in} \right)}.}}} & \left( {{Eq}.\mspace{14mu} 30} \right) \end{matrix}$

because the lowest order is influenced only by the linear chirp. The corresponding effective focal distance f_(eff) is given in first approximation by the distance that a beam needs to propagate to the beam center.

$\begin{matrix} {{\left( {{C_{0} \cdot f_{eff}} + A_{0}} \right) \cdot x_{in}} = 0} & \left( {{Eq}.\mspace{14mu} 1} \right) \\ {\left. \Rightarrow f_{eff} \right. = \frac{{- \cos^{2}}\psi_{out}}{{a_{g}\left( {{\sin \; \psi_{in}} - {\sin \; \psi_{out}}} \right)}^{2}}} & \left( {{Eq}.\mspace{14mu} 2} \right) \end{matrix}$

However a_(g) has to remain zero, since the focus of the beam is not the goal, because the behavior of the lowest order for a quadratic chirp b_(g) is important. Of all matrix elements, only the focusing element c(x_(in)) is modified, so that the angular dispersion is proportional to x_(in):

$\begin{matrix} {{C\left( x_{in} \right)} = {{x_{in}\underset{\underset{C_{1}}{}}{\left( {{4b_{g}} + {4b_{g}{\cos \left( {2\psi_{out}} \right)}}} \right) \cdot \frac{\left( {{\tan \; \psi_{in}} - {\sin \; {\psi_{out}/\cos}\; \psi_{in}}} \right)^{2}}{8\cos^{3}\psi_{out}}}} + {O\left( x_{in}^{2} \right)}}} & \left( {{Eq}.\mspace{14mu} 3} \right) \end{matrix}$

Applied to a laser beam with a spatial dispersion, this leads to an additional angular dispersion, which varies linearly across the entire beam diameter;

AD(x _(in))=AD ₀ +SD ₀ C ₁ ·x _(in)  (Eq. 34)

Requiring a pulse front tilt to φ/2 is defined in a first approximation, by the grating properties.

ψ=acrsin(cos ψ_(out)(tan ψ_(out)−tan φ/2))  (Eq. 35)

The stretcher-compressor combination at the beginning of the development ensures that disappear in a first approximation GDD and SD in line focus, so that applies together with (Eq. 35) in the first approximation for the pre-compensation of spatial dispersion SD

$\begin{matrix} {{SD}_{0} = {\frac{\partial x_{out}}{{\partial\Delta}\; v} = {\frac{L_{0}\lambda_{0}\tan \; {\varphi/2}}{{c \cdot \cos}\; \psi_{out}}\sqrt{{\cos \left( {\varphi - \psi_{out}} \right)}\cos \; {\psi_{out}/\cos^{2}}{\varphi/2}}}}} & \left( {{Eq}.\mspace{14mu} 36} \right) \end{matrix}$

and for group delay dispersion GDD

$\begin{matrix} {{GDD}_{0} = {\frac{{\partial\Delta}\; t}{{\partial\Delta}\; v} = {L_{0}{\lambda_{0}/c^{2}}\tan^{2}\; {\varphi/2.}}}} & \left( {{Eq}.\mspace{14mu} 37} \right) \end{matrix}$

The output angle ψ_(out) is determined according to the above two equations

ψ_(out)<π/2−φ  (Eq. 38)

and the grating spacing d₀ is determined by the grating equation

d0=λ₀/(sin ψ_(out)−sin ψ_(in)).  (Eq. 39)

To fulfill equitation (Eq. 3), a grating spacing

d(s)=d ₀ +b _(g)λ₀ s ²  (Eq. 40)

is assumed as a correction to first order, which is follows along its surface coordinate of a square dependence.

Using extending the Kostenbauder formalisms to a higher order and the calculation of the spatial dispersion SD(x_(in))=∂x_(out)(x_(in),Δv)/∂Δv in the interaction region by a distance L₀ in transversal beam coordinates x_(in) higher equation (Eq. 3) is obtained to:

$\begin{matrix} {\frac{{SD}\left( x_{in} \right)}{x_{out}\left( x_{in} \right)} = {{{AD}\left( x_{in} \right)} \cdot \left( {{\tan \left( {{\pi/2} - \varphi} \right)} + {\tan \left( {\varphi/2} \right)}} \right)}} & \left( {{Eq}.\mspace{14mu} 41} \right) \end{matrix}$

The higher order dispersion is neglected and the quadratic chirp of the grating line spacing is calculated to

$\begin{matrix} {{b_{g} = {- \frac{\cos \; {\psi_{out} \cdot \left( {{\tan \left( {{\pi/2} - \varphi} \right)} + {\tan \; {\varphi/2}}} \right)}}{2L_{0}^{2}{\tan \;}^{2}{\varphi/2}}}},} & \left( {{Eq}.\mspace{14mu} 4} \right) \end{matrix}$

The above calculations use a grid function of the second order (quadratic profile VLS), although other grid functions can be used to achieve a similar effect. The only remaining degrees of freedom in this design are now the length L₀ between the VLS grating and the line focus, as well as the outgoing angle ψ_(out). Using this remaining parameter space dispersion conditions (Eq. 3) to (Eq. 6) should be calculated and subsequently should be minimized. The equations (Eq. 39), (Eq. 40) and (Eq. 42) describe a possible implementation of a VLS-grating as a dispersive element. Thus, not only the compensation of the above dispersion conditions will be achieved at a particular time in a particular place, but in the whole interaction region.

The arrangement is not limited to collimated rays.

A further advantageous embodiment of the dispersive element is the use of an optical grating with a uniform grating spacing (FIG. 5 a) in combination with a high-precision, deformed mirror so that the so-curved mirror surface have beam imaging properties which corresponding to those of the grating with a varying grating spacing (FIG. 5 b).

Also possible is using a mirror which has both properties, the combination of a mirror with high-precision image ended radiant properties and of the focusing mirror.

Another embodiment of the arrangement is that the in one direction focusing optical element and the dispersive element can be replaced with a in one direction focusing optical element, wherein the in one direction focusing optical element is processed such that it additionally comprises the features of an optical grating non-uniform grid spacing, such e.g., a mirror is coated an optical grating with non-uniform grating spacing.

As focusing optical elements can not only used mirror, but for special applications lenses are possible.

The above arrangement is not only limited to the use of electron sources. Other suitable radiation or particle sources should be used.

One use of the above arrangement is the generation of directed radiation of a certain wavelength. Here, the pulse front tilt of the laser pulse and the overlap angle between the electron beam and the laser beam are used. The pulse duration of the emitted short wave light pulse is only limited by the duration of the electron pulse, the minimum wavelength of the energy of the electrons. Moreover, the bandwidth of the radiation can be determined by appropriate choice of the local field intensity of the laser pulse in the interaction area, and by the length of the laser line focus. In addition, the temporal and/or spatial coherence properties are adjusted by means of varying the laser pulse front tilt. This allows for the design of a suitable light source for a specific application if the desired radiation properties such as maximum power and coherence, are fixed. A customized combination of laser and electron source, reflection gratings and cylindrical mirrors may be calculated.

The achievable high photon numbers in ultra-short pulses of high brilliance in principle tunable wavelengths from EUV to hard X-rays provide unique diagnostic techniques and methods in research and industry, such as pump-probe experiments with X-rays on ultrashort time scales, structural analysis of single molecules, superconductivity research, and time-resolved diagnostics of processes in dense, hot plasmas.

Compared to synchrotrons and free electron lasers, these sources are compact, cost-effective and thus attractive for universities, research institutes and companies. This is made possible by the relative lower electron energies and thereby smaller electron accelerators. Especially in combination with laser-accelerated electrons, systems feasible in laboratory size may be completely optically controlled and synchronized.

One application provides in the field of EUV lithography, the inventive arrangement replaces previously scheduled free electron laser (FEL). The use of an FEL shows in concept studies [Socol, Y.: 13.5-nm EUV Lithography for Free Electron Laser. Proceedings of the FEL Conference, 2010] that the necessary photon yield can be achieved but it is very cost intensive. Our inventive arrangement, shown in FIG. 7, is a less expensive alternative.

As shown in FIG. 7, electrons are accelerated to the target energy in a highly repetitive electron storage ring with a high average current to realize radiation in the EUV range in a by TWTS realized compact electron laser. The required average radiation power is achieved through a high level of repetition of both the electron source, as well as the laser. The required intensity at high repetition rate is achieved by a resonator. It is necessary, the dispersion in the resonator periodically again with the help of at least one other dispersive element. Compared to previous approaches, which provide for a conventional free electron laser, this approach has the advantage that it works with lower electron energies, and thus the electron accelerator and the FEL on a much smaller scale and can be implemented so that a lower cost. Unlike discharge and plasma sources, no debris is created here.

Another possible application is suitable for the investigation of materials using phase-contrast imaging. In this method, in contrast to conventional X-ray imaging method, the absorption coefficient of a material is not used, but the index of refraction n of the material in the corresponding X-ray range. As (n−1) is higher by orders of magnitude, than the absorption coefficient, interferometry methods, which use the local refractive index, are much more sensitive than the conventional absorption method.

This makes it possible to investigate small structures in solids (e.g. microscopic fissures in parts production) and soft organic matter (e.g. as organs). Due to the better contrast and lower dose to diagnostic applications, applications in radiology are feasible, wherein, a significant medical use here the mammographic screening for breast cancer. For this process, spatial and temporal coherence conditions must be met, which is why high-quality images were obtained with a short recording time been predominantly produced by synchrotron sources.

Another possible application opens up when media (e.g. solids, plasmas, etc.) may be used instead of the particle beam. In laser technology, for example, there is the possibility to pump elongated laser media (laser rods) by side and therefore avoid disadvantages such as short relaxation time of the laser medium, non-linear propagation effects and/or amplified spontaneous emission (ASE).

TWTS may also be used for non-radiative processes, e.g. to excite efficiently weak transitions in relativistic ion beams. In this case, the pump wavelength may be specifically and accurately defined by the interaction angle or the ion energy.

Another possible application is the radiative electron or equivalent positron cooling. In an electron storage ring in this case, the Thomson or the Compton scattering is not primarily used as a source of light. Instead, the recoil of the emitted x-ray radiation on the electrons in the scattering process, and subsequently carried out re-acceleration are used to cool over many scattering events to the electron pulse gradually in order to achieve previously unattained beam properties.

Due to the high number of required per electron scattering processes, the needed arrangement is similar to the arrangement for EUV lithography (see FIG. 7), with the difference that TWTS must not be operated as a FEL here.

This here described process/method and the special arrangement stand out from competing methods for generating short-wave, ultrashort light pulses, and thus are more uses conceivable:

-   -   Using today known high-performance short-pulse lasers, single         shot photon numbers can be produced with TWTS a low-bandwidth         windows, which are several orders of magnitude higher than what         current Thomson backscatter sources provide a comparable range         and comparable laser parameters. TWTS-based sources can compete         in their single-shot performance with classical FEL-based         sources of the latest generation (FLASH), but are much more         compact, less complex to implement in the design and cost.     -   The photon energy of a TWTS-source may be selected or set within         a wide range by appropriate choice of pulse front tilt. This         tunability goes far beyond the capabilities of conventional,         accelerator-based sources and requires relatively little         investment in suitable optical gratings.     -   The TWTS process is a purely optical method; therefore no         adverse effects occur, such as unwanted induced fields in         classical Undulator structures at high electron pulse charges.     -   TWTS sources by using suitable electron sources with low         emittance and high peak load time as delivering spatially         coherent pulsed radiation, the properties of the so-called         radiation FELs match.     -   The bandwidth of the radiation can be adjusted by suitable         choice of the interaction length.     -   The properties, determined by TWTS, to the used electron pulses,         such as pulse energy, pulse length, or emittance are         significantly lower than those of comparable sources such         table-top SASE FELs.     -   TWTS-radiation is produced by radiation of electron pulses         relativistic energy and is emitted therefore directed to a small         solid angle.     -   The interaction range can be scaled up to larger optics and beam         diameters.     -   TWTS is suitable for high vacuum applications and produces no         debris, which reduces the lifetime inserted optics.     -   TWTS may be used to generate, to stimulate or to pump rapidly         propagating waves, suggestions or modes in the line focus on         media (e.g. gas, solid state, cluster, plasma, liquid or gaseous         smoked media).     -   TWTS may be used for radiative cooling of particle beams,         wherein the used arrangement is smaller than previous         arrangements, it is easier to manufacture, and the interaction         distance is longer or the dispersion can be controlled.

REFERENCE SYMBOLS

-   GDD group delay dispersion -   SD spatial dispersion -   AD angular dispersion -   1 interaction at the beginning -   2 interaction in the middle and -   3 interaction at the end of the overlay -   4 propagation direction -   5 resulting light pulse -   6 electrons -   7 laser pulse -   8 focus along the electron trajectory -   9 in a direction focusing optical element -   10 dispersive element (e.g. VLS grating) -   11 laser system with stretcher and/or compressor -   13 output direction -   14 input reference plane -   15 Output reference plane -   17 acceleration route -   18 inventive arrangement, the (TWTS) system -   19 resonator, superevaluation cavity -   20 incoming laser beams -   21 electron injector -   22 beam dump -   23 storage ring -   24 resulting (EUV) radiation -   25 wavefront 

1-16. (canceled)
 17. An apparatus for generating ultra-short short-wave light pulses, the apparatus comprising: a laser system; a source for electrons, particles or radiation, said laser system and said source being synchronized; one or more optical elements for focusing in one direction and one or more dispersive elements disposed along a laser beam profile between said laser system and an overlap region, wherein said one or more of optical elements and said one or more dispersive elements are arranged in an arbitrary order, to thereby configure an optimum temporal and spatial pulse compression in the overlap region for an interaction region of a few millimeters and up to several meters in length.
 18. The apparatus according to claim 17, wherein said focusing element for focusing in one direction is selected from the group consisting of a cylindrical mirror, a toroidal mirror, and a corresponding lens.
 19. The apparatus according to claim 17, wherein said dispersive element is a diffraction grating with non-uniform grating spacings.
 20. The apparatus according to claim 17, wherein: said dispersive element consists of an optical grating with a uniform grating spacing and a beam imaging optical element wherein a curved surface of said beam imaging optical element is produced to additionally have the characteristics of an optical grating with non-uniform grating spacing; or said dispersive element is an optical grating with uniform grating spacings, and said focusing element for focusing in one direction is processed to additionally have the characteristics of a beam imaging optical element.
 21. The apparatus according to claim 17, wherein said optical element for focusing in one direction and said dispersive element are one element formed as the element focusing in one direction produced to additionally have the properties of an optical grating with non-uniform grating spacing.
 22. A method, which comprises providing the apparatus according to claim 17 and superimposing therewith a pulse front tilt light pulse of high power with an ultra-short pulse of relativistic electrons in a laser line focus.
 23. The method according to claim 22, which comprises employing the apparatus in EUV lithography to replace a compact free-electron laser.
 24. The method according to claim 22, which comprises employing the apparatus for optimizing properties of the laser pulse.
 25. The method according to claim 22, which comprises varying an emitted radiation wavelength by a choice of the pulse front tilt and an angle between electron beam and laser beam.
 26. The method according to claim 22, wherein, when the interaction length is increased a number of emitted photons per pulse increases.
 27. The method according to claim 22, which comprises varying a bandwidth of the laser pulse by changing a length of the line focuses and/or a laser field intensity in the interaction region between the electron beam and laser beam.
 28. The method according to claim 22, which comprises varying a size of the central interaction region by changing one or both of a duration of the laser pulse or a grating spacing.
 29. The method according to claim 22, which comprises emitting temporally coherent radiation, spatially coherent radiation, or temporally and spatially coherent radiation.
 30. The method according to claim 22, which comprises generating, exciting, or pumping rapidly propagating waves, excitations, or modes in media in line focus.
 31. The method according to claim 22, which comprises controlling a spatial chirp along the length of the interaction region.
 32. The method according to claim 22, which comprises providing the dispersive element as a grating with a uniform grating spacing, and employing the apparatus as a free-electron laser. 